On top of that, there is the third statement, representing the
general feature of QFT and valid, in particular, for QG. The
counterterms required to remove UV divergences, in all loop
orders, are local functionals of the fields. The mathematically
rigid proof of this statement (usually called Weinberg's theorem
[1]}) is complicated and can be found, e.g., in
[2]}. In what follows, we shall apply these three
statement to describe the renormalization in QG.
